TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas T1 - The Quickest Path to the Goal N2 - We provide an introduction into the mathematics of and with paths. Not on the shortest, but hopefully on an entertaining path! T3 - ZIB-Report - 10-21 KW - shortest paths KW - combinatorial optimization KW - operations research Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11840 SN - 1438-0064 ER - TY - GEN A1 - Schlechte, Thomas A1 - Tanner, Andreas T1 - Railway capacity auctions with dual prices N2 - Railway scheduling is based on the principle of the construction of a conflict-free timetable. This leads to a strict definition of capacity: in contrast with road transportation, it can be said in advance whether a given railway infrastructure can accommodate - at least in theory - a certain set of train requests. Consequently, auctions for railway capacity are modeled as auctions of discrete goods -- the train slots. We present estimates for the efficiency gain that may be generated by slot auctioning in comparison with list price allocation. We introduce a new class of allocation and auction problems, the feasible assignment problem, that is a proper generalization of the well-known combinatorial auction problem. The feasible assignment class was designed to cover the needs for an auction mechanism for railway slot auctions, but is of interest in its own right. As a practical instance to state and solve the railway slot allocation problem, we present an integer programming formulation, briefly the ACP, which turns out to be an instance of the feasible assignment problem and whose dual problem yields prices that can be applied to define a useful activity rule for the linearized version of the Ausubel Milgrom Proxy auction. We perform a simulation aiming to measure the impact on efficiency and convergence rate. T3 - ZIB-Report - 10-10 KW - Combinatorial Auction Problem KW - Railway Track Allocation KW - Ausubel Milgrom Proxy Auction Mechanism Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11729 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Dovica, Ivan A1 - Nowak, Ivo A1 - Schickinger, Thomas T1 - Robust Tail Assignment N2 - We propose an efficient column generation method to minimize the probability of delay propagations along aircraft rotations. In this way, delay resistant schedules can be constructed. Computational results for large-scale real-world problems demonstrate substantial punctuality improvements. The method can be generalized to crew and integrated scheduling problems. T3 - ZIB-Report - 10-08 KW - Flugzeugumlaufplanung KW - robuste Optimierung KW - Spaltenerzeugung KW - Tail Assignment KW - Robust Optimization KW - Column Generation Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11707 SN - 1438-0064 ER - TY - GEN A1 - Frank, Martin A1 - Fügenschuh, Armin A1 - Herty, Michael A1 - Schewe, Lars T1 - The Coolest Path Problem N2 - We introduce the coolest path problem, which is a mixture of two well-known problems from distinct mathematical fields. One of them is the shortest path problem from combinatorial optimization. The other is the heat conduction problem from the field of partial differential equations. Together, they make up a control problem, where some geometrical object traverses a digraph in an optimal way, with constraints on intermediate or the final state. We discuss some properties of the problem and present numerical solution techniques. We demonstrate that the problem can be formulated as a linear mixed-integer program. Numerical solutions can thus be achieved within one hour for instances with up to 70 nodes in the graph. T3 - ZIB-Report - 09-37 Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11571 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika T1 - Models for Line Planning with Transfers N2 - We propose a novel integer programming approach to transfer minimization for line planning problems in public transit. The idea is to incorporate penalties for transfers that are induced by “connection capacities” into the construction of the passenger paths. We show that such penalties can be dealt with by a combination of shortest and constrained shortest path algorithms such that the pricing problem for passenger paths can be solved efficiently. Connection capacity penalties (under)estimate the true transfer times. This error is, however, not a problem in practice. We show in a computational comparison with two standard models on a real-world scenario that our approach can be used to minimize passenger travel and transfer times for large-scale line planning problems with accurate results. T3 - ZIB-Report - 10-11 KW - Linienplanung KW - Umsteigen KW - Ganzzahlige Programmierung KW - Kombinatorische Optimierung KW - line planning KW - transfers KW - integer programming KW - combinatorial optimization Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11742 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - A Case Study on Optimizing Toll Enforcements on Motorways N2 - In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to feasible rosters for one month. We present computational results in a case-study on a German subnetwork which documents the practicability of our approach. T3 - ZIB-Report - 12-21 KW - Vehicle Routing Problem KW - Duty Rostering KW - Integer Programming KW - Operations Research Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15498 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Cardonha, Carlos T1 - A Set Partitioning Approach to Shunting N2 - The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem in public transport planning. A number of models and approaches have been suggested in the literature, which work for small problems, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation solution approach for the VPP. The model provides a tight linear description of the problem. The pricing problem, and hence the LP relaxation itself, can be solved in polynomial resp. pseudo-polynomial time for some versions of the problems. T3 - ZIB-Report - 09-18 KW - integer programming KW - set partitioning KW - combinatorial packing KW - vehicle positioning Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11326 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc T1 - Nonlinear pseudo-Boolean optimization: relaxation or propagation? N2 - Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver. T3 - ZIB-Report - 09-11 KW - Pseudo-Boolean KW - constraint integer programming KW - linear relaxation KW - separation algorithm KW - domain propagation Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11232 SN - 1438-0064 ER - TY - GEN A1 - Heinz, Stefan A1 - Stephan, Rüdiger A1 - Schlechte, Thomas T1 - Solving Steel Mill Slab Problems with Branch and Price N2 - The steel mill slab design problem from the CSPLib is a binpacking problem that is motivated by an application of the steel industry and that has been widely studied in the constraint programming community. Recently, several people proposed new models and methods to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called multiple knapsack problem with color constraints, originated from the same industrial problem, were discussed in the integer programming community. In particular, a simple integer programming for this problem has been given by Forrest et al. [3]. The aim of this paper is to bring these different studies together. Moreover, we adopt the model of [3] for the steel mill slab problem. Using a state of the art integer program solver, this model is capable to solve all instances of the steel mill slab library, mostly in less than one second, to optimality. We improved, thereby, the solution value of 76 instances. T3 - ZIB-Report - 09-14 KW - steel mill slab problem KW - branch-and-price KW - integer programming Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11260 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf T1 - Discrete Optimization in Public Transportation N2 - The mathematical treatment of planning problems in public transit has made significant advances in the last decade. Among others, the classical problems of vehicle and crew scheduling can nowadays be solved on a routine basis using combinatorial optimization methods. This is not yet the case for problems that pertain to the design of public transit networks, and for the problems of operations control that address the implementation of a schedule in the presence of disturbances. The article gives a sketch of the state and important developments in these areas, and it addresses important challenges. The vision is that mathematical tools of computer aided scheduling (CAS) will soon play a similar role in the design and operation of public transport systems as CAD systems in manufacturing. N2 - Die mathematische Behandlung von Planungsproblemen im öffentlichen Verkehr hat im letzten Jahrzehnt große Fortschritte gemacht. Klassische Probleme wie die Umlauf- und die Dienstplanung können heutzutage routinemäßig mit kombinatorischen Optimierungsmethoden gelöst werden. Die Behandlung von Problemen der Angebotsplanung und der Betriebssteuerung sind dagegen noch nicht ganz auf diesem Stand. Dieser Artikel gibt einen Überblick über den Stand der Forschung, über wichtige Entwicklungen und einige Herausforderungen in diesem Gebiet. Die Vision ist, dass mathematische Planungswerkzeuge im öffentlichen Verkehr (Computer Aided Scheduling, CAS) in Zukunft eine ähnliche Rolle spielen werden wie CAD-Systeme in der industriellen Fertigung. T3 - ZIB-Report - 08-56 KW - Öffentlicher Verkehr KW - Nahverkehr KW - Optimierung KW - Public Transit KW - Optimization Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11207 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoang, Nam-Dung T1 - Fair Ticket Prices in Public Transport N2 - Ticket pricing in public transport usually takes a welfare or mnemonics maximization point of view. These approaches do not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and integer programming. An application to pricing railway tickets for the intercity network of the Netherlands demonstrates that, in this sense, prices that are much fairer than standard ones can be computed in this way. T3 - ZIB-Report - 08-46 KW - Ticket prices KW - cost allocation game Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10999 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Dittbrenner, Bastian A1 - Langenhan, Andreas A1 - Seidl, Stephan A1 - Weider, Steffen T1 - Integrierte Dienst- und Dienstreihenfolgeplanung zur Erhöhung der Fahrerzufriedenheit N2 - Wir stellen einen mathematischen Optimierungsansatz zur integrierten Dienst- und Dienstreihenfolgeplanung im öffentlichen Nahverkehr vor, mit dem sich bei konstanten Personalkosten die Fahrerzufriedenheit deutlich steigern lässt. T3 - ZIB-Report - 14-02 KW - duty scheduling KW - duty rostering KW - integrated scheduling KW - Benders' decomposition Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50270 SN - 1438-0064 ER - TY - GEN A1 - Heismann, Olga A1 - Borndörfer, Ralf T1 - A Generalization of Odd Set Inequalities for the Set Packing Problem N2 - The set packing problem, sometimes also called the stable set problem, is a well-known NP-hard problem in combinatorial optimization with a wide range of applications and an interesting polyhedral structure, that has been the subject of intensive study. We contribute to this field by showing how, employing cliques, odd set inequalities for the matching problem can be generalized to valid inequalities for the set packing polytope with a clear combinatorial meaning. T3 - ZIB-Report - 14-28 KW - set packing KW - matching KW - hypergraph KW - inequality KW - facet Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-51010 SN - 1438-0064 ER - TY - THES A1 - Heismann, Olga T1 - The Hypergraph Assignment Problem N2 - This thesis deals with the hypergraph assignment problem (HAP), a set partitioning problem in a special type of hypergraph. The HAP generalizes the assignment problem from bipartite graphs to what we call bipartite hypergraphs, and is motivated by applications in railway vehicle rotation planning. The main contributions of this thesis concern complexity, polyhedral results, analyses of random instances, and primal methods for the HAP. We prove that the HAP is NP-hard and APX-hard even for small hyperedge sizes and hypergraphs with a special partitioned structure. We also study the complexity of the set packing and covering relaxations of the HAP, and present for certain cases polynomial exact or approximation algorithms. A complete linear description is known for the assignment problem. We therefore also study the HAP polytope. There, we have a huge number of facet-defining inequalities already for a very small problem size. We describe a method for dividing the inequalities into equivalence classes without resorting to a normal form. Within each class, facets are related by certain symmetries and it is sufficient to list one representative of each class to give a complete picture of the structural properties of the polytope. We propose the algorithm "HUHFA" for the classification that is applicable not only to the HAP but combinatorial optimization problems involving symmetries in general. In the largest possible HAP instance for which we could calculate the complete linear description, we have 14049 facets, which can be divided into 30 symmetry classes. We can combinatorially interpret 16 of these classes. This is possible by employing cliques to generalize the odd set inequalities for the matching problem. The resulting inequalities are valid for the polytope associated with the set packing problem in arbitrary hypergraphs and have a clear combinatorial meaning. An analysis of random instances provides a better insight into the structure of hyperassignments. Previous work has extensively analyzed random instances for the assignment problem theoretically and practically. As a generalization of these results for the HAP, we prove bounds on the expected value of a minimum cost hyperassignment that uses half of the maximum possible number of hyperedges that are not edges. In a certain complete partitioned hypergraph G2,2n with i. i. d. exponential random variables with mean 1 as hyperedge costs it lies between 0.3718 and 1.8310 if the vertex number tends to infinity. Finally, we develop an exact combinatorial solution algorithm for the HAP that combines three methods: A very large-scale neighborhood search, the composite columns method for the set partitioning problem, and the network simplex algorithm. N2 - Diese Arbeit beschäftigt sich mit dem Hypergraph Assignment Problem (Abkürzung "HAP", dt.: Zuordnungsproblem auf Hypergraphen), einem Mengenzerlegungsproblem auf einem speziellen Typ von Hypergraphen. Das HAP verallgemeinert das Zuordnungsproblem von bipartiten Graphen auf eine Struktur, die wir bipartite Hypergraphen nennen, und ist durch eine Anwendung in der Umlaufplanung im Schienenverkehr motiviert. Die Hauptresultate betreffen die Komplexität, polyedrische Ergebnisse, die Analyse von Zufallsinstanzen sowie primale Methoden für das HAP. Wir beweisen, dass das HAP NP-schwer und APX-schwer ist, sogar wenn wir uns auf kleine Hyperkantengrößen und Hypergraphen mit einer speziellen, partitionierten Struktur beschränken. Darüber hinaus untersuchen wir die Komplexität der Mengenpackungs- sowie Mengenüberdeckungsrelaxierung und geben für bestimmte Fälle Approximations- und exakte Algorithmen mit einer polynomiellen Laufzeit an. Für das Polytop des Zuordnungsproblems ist eine vollständige lineare Beschreibung bekannt. Wir untersuchen daher auch das HAP-Polytop. Dafür ist die Anzahl der Facettenungleichungen schon für sehr kleine Problemgrößen sehr groß. Wir beschreiben eine Methode zur Aufteilung der Ungleichungen in Äquivalenzklassen, die ohne die Verwendung von Normalformen auskommt. Die Facetten in jeder Klasse können durch Symmetrien ineinander überführt werden. Es genügt, einen Repräsentanten aus jeder Klasse anzugeben, um ein vollständiges Bild der Polytopstruktur zu erhalten. Wir beschreiben den Algorithmus "HUHFA", der diese Klassifikation nicht nur für das HAP, sondern für beliebige kombinatorische Optimierungsprobleme, die Symmetrien enthalten, durchführt. Die größtmögliche HAP-Instanz, für die wir die vollständige lineare Beschreibung berechnen konnten, hat 14049 Facetten, die in 30 Symmetrieklassen aufgeteilt werden können. Wir können 16 dieser Klassen kombinatorisch interpretieren. Dafür verallgemeinern wir Odd-Set-Ungleichungen für das Matchingproblem unter Verwendung von Cliquen. Die Ungleichungen, die wir erhalten, sind gültig für Mengenpackungsprobleme in beliebigen Hypergraphen und haben eine klare kombinatorische Bedeutung. Die Analyse von Zufallsinstanzen erlaubt einen besseren Einblick in die Struktur von Hyperzuordnungen. Eine solche ausführliche Analyse wurde in der Literatur theoretisch und praktisch bereits für das Zuordnungsproblem durchgeführt. Als eine Verallgemeinerung dieser Ergebnisse für das HAP beweisen wir Schranken für den Erwartungswert einer Hyperzuordnung mit minimalen Kosten, die genau die Hälfte der maximal möglichen Anzahl an Hyperkanten, die keine Kanten sind, benutzt. In einem sog. vollständigen partitionierten Hypergraphen G2,2n mit Hyperkantenkosten, die durch unabhängig identisch exponentiell verteilte Zufallsvariablen mit Erwartungswert 1 bestimmt sind, liegt dieser Wert zwischen 0.3718 und 1.8310, wenn die Knotenanzahl gegen unendlich strebt. Schließlich entwickeln wir eine exakte kombinatorische Lösungsmethode für das HAP, die drei Ansätze kombiniert: Eine Nachbarschaftssuche mit Nachbarschaften exponentieller Größe, die Composite-Columns-Methode für das Mengenzerlegungsproblem sowie den Netzwerksimplexalgorithmus. KW - assignment KW - bipartite KW - hyperassignment KW - hypergraph KW - set partitioning Y1 - 2014 UR - http://opus4.kobv.de/opus4-tuberlin/frontdoor/index/index/docId/5321 ER - TY - GEN A1 - Gamrath, Gerald A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Winkler, Michael T1 - Structure-based primal heuristics for mixed integer programming N2 - Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They help to reach optimality faster and provide good feasible solutions early in the solving process. In this paper, we present two new primal heuristics which take into account global structures available within MIP solvers to construct feasible solutions at the beginning of the solving process. These heuristics follow a large neighborhood search (LNS) approach and use global structures to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. The definition of the neighborhood is done by iteratively fixing variables and propagating these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. The neighborhood is solved as a sub-MIP and solutions are transferred back to the original problem. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about every third instance and therewith help to improve the average solving time. T3 - ZIB-Report - 15-26 KW - mixed-integer programming, large neighborhood search, primal heuristics, domain propagation Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55518 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Timetabling and Passenger Routing in Public Transport T2 - Appeard in: Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015) N2 - The task of timetabling is to schedule the trips in a public transport system by determining periodic arrival and departure times at every station. The goal is to provide a service that is both attractive for passengers and can be operated economically. To date, timetable optimization is generally done with respect to fixed passenger routes, i.e., it is assumed that passengers do not respond to changes in the timetable. This is unrealistic and ignores potentially valuable degrees of freedom. We investigate in this paper periodic timetabling models with integrated passenger routing. We propose several models that differ in the allowed passenger paths and the objectives. We compare these models theoretically and report on computations on real-world instances for the city of Wuppertal. T3 - ZIB-Report - 15-31 KW - Passenger routing KW - Periodic timetabling KW - Public transport Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55305 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Winkler, Michael T1 - Structure-driven fix-and-propagate heuristics for mixed integer programming N2 - Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early in the solving process and help to solve instances to optimality faster. In this paper, we present a scheme for primal start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved as an LP and the solution is rounded. If the rounded solution did not provide a feasible solution already, a sub-MIP is solved for the neighborhood defined by the variable fixings performed in the first phase. The global structures help to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about three out of five instances and therewith help to improve several performance measures for MIP solvers, including the primal integral and the average solving time. T3 - ZIB-Report - 17-56 KW - mixed-integer programming KW - primal heuristics KW - fix-and-propagate KW - large neighborhood search KW - domain propagation Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65387 SN - 1438-0064 ER - TY - GEN A1 - Karbstein, Marika T1 - Integrated Line Planning and Passenger Routing: Connectivity and Transfers N2 - The integrated line planning and passenger routing problem is an important planning problem in service design of public transport. A major challenge is the treatment of transfers. A main property of a line system is its connectivity. In this paper we show that analysing the connecvitiy aspect of a line plan gives a new idea to handle the transfer aspect of the line planning problem. T3 - ZIB-Report - 14-42 KW - line planning, transfers,Steiner connectivity problem Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-52986 SN - 1438-0064 ER - TY - GEN A1 - Heinz, Stefan A1 - Beck, J. Christopher T1 - Reconsidering Mixed Integer Programming and MIP-based Hybrids for Scheduling N2 - Despite the success of constraint programming (CP) for scheduling, the much wider penetration of mixed integer programming (MIP) technology into business applications means that many practical scheduling problems are being addressed with MIP, at least as an initial approach. Furthermore, there has been impressive and well-documented improvements in the power of generic MIP solvers over the past decade. We empirically demonstrate that on an existing set of resource allocation and scheduling problems standard MIP and CP models are now competitive with the state-of-the-art manual decomposition approach. Motivated by this result, we formulate two tightly coupled hybrid models based on constraint integer programming (CIP) and demonstrate that these models, which embody advances in CP and MIP, are able to out-perform the CP, MIP, and decomposition models. We conclude that both MIP and CIP are technologies that should be considered along with CP for solving scheduling problems. T3 - ZIB-Report - 12-05 KW - constraint integer programming KW - constraint programming KW - cumulative constraint KW - mixed integer programming KW - optional activities Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14660 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Rapid Branching N2 - We propose rapid branching (RB) as a general branch-and-bound heuristic for solving large scale optimization problems in traffic and transport. The key idea is to combine a special branching rule and a greedy node selection strategy in order to produce solutions of controlled quality rapidly and efficiently. We report on three successful applications of the method for integrated vehicle and crew scheduling, railway track allocation, and railway vehicle rotation planning. T3 - ZIB-Report - 12-10 KW - large scale optimization KW - rapid branching KW - column generation Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14728 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Vehicle Rotation Planning for Intercity Railways N2 - This paper provides a generic formulation for rolling stock planning problems in the context of intercity passenger traffic. The main contributions are a graph theoretical model and a Mixed-Integer-Programming formulation that integrate all main requirements of the considered Vehicle-Rotation-Planning problem (VRPP). We show that it is possible to solve this model for real-world instances provided by our industrial partner DB Fernverkehr AG using modern algorithms and computers. T3 - ZIB-Report - 12-11 KW - rolling-stock-planning KW - mixed-integer-programming KW - hypergraphs KW - column generation KW - rapid branching Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14731 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Langenhan, Andreas A1 - Löbel, Andreas A1 - Schulz, Christof A1 - Weider, Steffen T1 - Duty Scheduling Templates N2 - We propose duty templates as a novel concept to produce similar duty schedules for similar days of operation in public transit. Duty templates can conveniently handle various types of similarity requirements, and they can be implemented with ease using standard algorithmic techniques. They have produced good results in practice. T3 - ZIB-Report - 12-09 KW - duty scheduling KW - duty templates Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14699 SN - 1438-0064 ER - TY - GEN A1 - Bestuzheva, Ksenia A1 - Besançon, Mathieu A1 - Chen, Wei-Kun A1 - Chmiela, Antonia A1 - Donkiewicz, Tim A1 - van Doornmalen, Jasper A1 - Eifler, Leon A1 - Gaul, Oliver A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - van der Hulst, Rolf A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc E. A1 - Rehfeldt, Daniel A1 - Schlein, Steffan A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Sofranac, Boro A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Wellner, Philipp A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 8.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack. T3 - ZIB-Report - 21-41 KW - Constraint integer programming KW - Linear programming KW - Mixed-integer linear programming KW - Mixed-integer nonlinear programming KW - Optimization solver KW - Branch-and-cut KW - Branch-and-price KW - Column generation KW - Parallelization KW - Mixed-integer semidefinite programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85309 SN - 1438-0064 ER - TY - GEN A1 - Bolusani, Suresh A1 - Besançon, Mathieu A1 - Bestuzheva, Ksenia A1 - Chmiela, Antonia A1 - Dionísio, João A1 - Donkiewicz, Tim A1 - van Doornmalen, Jasper A1 - Eifler, Leon A1 - Ghannam, Mohammed A1 - Gleixner, Ambros A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hedtke, Ivo A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - van der Hulst, Rolf A1 - Kamp, Dominik A1 - Koch, Thorsten A1 - Kofler, Kevin A1 - Lentz, Jurgen A1 - Manns, Julian A1 - Mexi, Gioni A1 - Mühmer, Erik A1 - E. Pfetsch, Marc A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Xu, Liding T1 - The SCIP Optimization Suite 9.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bug fixes. The SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. The SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver. T3 - ZIB-Report - 24-02-29 KW - Constraint integer programming KW - Linear programming KW - Mixed-integer linear programming KW - Mixed-integer nonlinear programming KW - Optimization solver KW - Branch-and-cut KW - Branch-and-price KW - Column generation KW - Parallelization KW - Mixed-integer semidefinite programming Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-95528 SN - 1438-0064 ER -